Out of sheer curiosity: Is there an actual application that requires reporting a number to 84 significant figures?
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JakeSep 14 '11 at 4:23

@Jake: See page 6 of this pdf which has 2000 decimal places to use in an unstable recursion. Page 8 has 200 decimal places of another number. In both cases there are 50 digits per line.
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HenrySep 14 '11 at 10:40

1

@Jake: Computation of the most possible digits of π for instance by far exceeds 84 digits: π. Quoting from Wikipedia: "One open question about π is whether it is a normal number—whether any digit block occurs in the expansion of π just as often as one would statistically expect if the digits had been produced completely 'randomly', and that this is true in every integer base, not just base 10." It even would seem the succession of digits is best described using chaos theory.
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Count ZeroSep 14 '11 at 22:50

Based on Peter Grill's answer, if you want the groups of digits to be aligned similarly the example in your question, you could switch off the indenting for the paragraph containing the number, pull back the first line by the width of the characters 0., and increase the left margin by the same amount. Wrapped into a macro, this could look like

In the following paragraph, you can see an absurdly long number, aligned in a pretty but meaningless way:
\printlongdecimal{0.123719283791283718927489749875289345793485723495234572935239452348952384573481234879}

will yield

Here's the full document:

\documentclass{article}
\usepackage{numprint}
\usepackage{bigintcalc}
\npdecimalsign{\ensuremath{.}}
\npthousandsep{\hspace{0.3em}}
\newlength{\widthofzeroandperiod}
\settowidth{\widthofzeroandperiod}{0.}
\newcommand{\printlongdecimal}[1]{
\raggedright%
\noindent%
\hspace{-\widthofzeroandperiod}%
\leftskip\widthofzeroandperiod%
\rightskip0.7\textwidth%
\numprint{#1}
}
\begin{document}
In the following paragraph, you can see an absurdly long number, aligned in a pretty but meaningless way:
\printlongdecimal{0.123719283791283718927489749875289345793485723495234572935239452348952384573481234879}
\end{document}

Use the numprint package. The \npdecimalsign is used to specify that the decimal separator is to be a period, and \npthousandsep{ } define a space as a separator for the thousands and this also allows for line breaks within the number.

Now this does not work with the article documentclass, the spaces become very wide. But there is a solution to everything! :) Either insert @{} in the definition of the columns: \begin{tabular}{c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c} - then you can directly control the spacing by replacing $\;$ with wathever other spacing you need or you can remove the columns containing the spacing characters ($\;$ in this example) altogether, leaving it to LaTeX to set the spacing.